MHB Is the function y = x + 2 one-to-one?

[mathdad]

Why is y = x + 2 one-to-one?

 

[skeeter]

Why is y = x + 2 one-to-one?

because every y-value in the range is generated by a single, unique input x-value in the domain

https://www.math.uh.edu/~jiwenhe/Math1432/lectures/lecture01_handout.pdf

 

[mathdad]

No matter what x is the value of y will be a different answer.

y = x + 2

Let x = 0

y = 0 + 2

y = 2

(0, 2)

Let x = 3

y = 3 + 2

y = 5

(3, 5)

Yes, for every x value, y has a different, unique answer.

So, it is one-to-one. It is also linear because the biggest power is 1.

Correct?

 

[skeeter]

fyi, using a few example function calculations does not confirm that a function is 1-1.

e.g. if you had "tested" using the same x-values with the function $y=\sqrt{9-x^2}$, you would have drawn an incorrect conclusion.

Having an idea of what the function graph looks like is important in determining things like domain, range, and whether or not a function is 1-1.

the function $y=\sqrt{9-x^2}$ is a semicircle of radius 3 in quadrants I and II ... it does not pass the horizontal line test.

 

[mathdad]

It is important to have a picture in mind of the basic functions to help determine if it is one-to-one or not.

When is an expression not a function?

 

[skeeter]

It is important to have a picture in mind of the basic functions to help determine if it is one-to-one or not.

When is an expression not a function?

come on, you know this ... when its graph doesn't pass the vertical line test

 

[mathdad]

Good information.